Identifier
Mp00023: Dyck paths to non-crossing permutationPermutations
Mp00072: Permutations binary search tree: left to rightBinary trees
Mp00014: Binary trees to 132-avoiding permutationPermutations
Mp00071: Permutations descent compositionInteger compositions
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-2
[1,0]=>[1]=>[.,.]=>[1]=>[1] [1,0,1,0]=>[1,2]=>[.,[.,.]]=>[2,1]=>[1,1] [1,1,0,0]=>[2,1]=>[[.,.],.]=>[1,2]=>[2] [1,0,1,0,1,0]=>[1,2,3]=>[.,[.,[.,.]]]=>[3,2,1]=>[1,1,1] [1,0,1,1,0,0]=>[1,3,2]=>[.,[[.,.],.]]=>[2,3,1]=>[2,1] [1,1,0,0,1,0]=>[2,1,3]=>[[.,.],[.,.]]=>[3,1,2]=>[1,2] [1,1,0,1,0,0]=>[2,3,1]=>[[.,.],[.,.]]=>[3,1,2]=>[1,2] [1,1,1,0,0,0]=>[3,2,1]=>[[[.,.],.],.]=>[1,2,3]=>[3] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,1,1,1] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,1,1] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,2,1] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,2,1] [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[3,1] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,1,2] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,2] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,1,2] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,1,2] [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,2] [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,3] [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,3] [1,1,1,0,1,0,0,0]=>[4,2,3,1]=>[[[.,.],[.,.]],.]=>[3,1,2,4]=>[1,3] [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>[4] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,1,1,1,1] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,1,1,1] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,1,1] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,1,1] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,1,1] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,1,2,1] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[2,2,1] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,1,2,1] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,1,2,1] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[2,2,1] [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,3,1] [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,3,1] [1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,3,1] [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[4,1] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,1,1,2] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,2] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,2,2] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,2,2] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,2] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,1,1,2] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,2] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,1,1,2] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,1,1,2] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,2] [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,2,2] [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,2,2] [1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[1,2,2] [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,2] [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,1,3] [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,3] [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,1,3] [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,1,3] [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,3] [1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[1,1,3] [1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[1,1,3] [1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[1,1,3] [1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[2,3] [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,4] [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,4] [1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[1,4] [1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[1,4] [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,1,1,1,1] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,1,1,1] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,1,1,1] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[3,1,1,1] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,1,2,1,1] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,2,1,1] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,1,2,1,1] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,1,2,1,1] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,2,1,1] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,3,1,1] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,3,1,1] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,3,1,1] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[4,1,1] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,1,1,2,1] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[2,1,2,1] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,2,2,1] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,2,2,1] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,2,1] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,1,1,2,1] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[2,1,2,1] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,1,1,2,1] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,1,1,2,1] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[2,1,2,1] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,2,2,1] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,2,2,1] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,2,2,1] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,2,1] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,1,3,1] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[2,3,1] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,1,3,1] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,1,3,1] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[2,3,1] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,1,3,1] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,1,3,1] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,1,3,1] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[2,3,1] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,4,1] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,4,1] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,4,1] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,4,1] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[5,1] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,1,1,1,2] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,1,2] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,2,1,2] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,2,1,2] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,2] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,1,2,2] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,2,2] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,1,2,2] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,1,2,2] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,2,2] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,3,2] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,3,2] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[1,3,2] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[4,2] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,1,1,1,2] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,1,2] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,2,1,2] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,2,1,2] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,2] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,1,1,1,2] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,1,2] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,1,1,1,2] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,1,1,1,2] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,1,2] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,2,1,2] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,2,1,2] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[1,2,1,2] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,2] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,1,2,2] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,2,2] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,1,2,2] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,1,2,2] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,2,2] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[1,1,2,2] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[1,1,2,2] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[1,1,2,2] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,2,2] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,3,2] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,3,2] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[1,3,2] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[1,3,2] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[4,2] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,1,1,3] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,1,3] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,2,3] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,2,3] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,3] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,1,1,3] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,1,3] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,1,1,3] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,1,1,3] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,1,3] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,2,3] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,2,3] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[1,2,3] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,3] [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,1,1,3] [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,1,3] [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,1,1,3] [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,1,1,3] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,1,3] [1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[1,1,1,3] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[1,1,1,3] [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[1,1,1,3] [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[2,1,3] [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[1,2,3] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[1,2,3] [1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[1,2,3] [1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[1,2,3] [1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[3,3] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,1,4] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,4] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,1,4] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,1,4] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,4] [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,1,4] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,1,4] [1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[1,1,4] [1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[2,4] [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,1,4] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,1,4] [1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[1,1,4] [1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[1,1,4] [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[2,4] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,5] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,5] [1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[1,5] [1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[1,5] [1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[1,5] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,1,2,1,1,1] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,2,1,1,1] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,1,2,1,1,1] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,1,2,1,1,1] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,2,1,1,1] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,3,1,1,1] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,3,1,1,1] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,3,1,1,1] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,1,1,1] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,1,2,1,1] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[3,2,1,1] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,1,2,1,1] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,1,2,1,1] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,2,1,1] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[3,2,1,1] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,1,3,1,1] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,3,1,1] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,1,3,1,1] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,1,3,1,1] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,3,1,1] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,1,3,1,1] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,1,3,1,1] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,1,3,1,1] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[2,3,1,1] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,4,1,1] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,4,1,1] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,4,1,1] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,4,1,1] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[5,1,1] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,1,2,1] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[2,2,2,1] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[2,2,2,1] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,1] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,1] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,1] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,2,1] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,1,2,1] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,2,1,2,1] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,1,2,1] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[2,2,2,1] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[2,2,2,1] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,1,2,2,1] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,1,2,2,1] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,1,2,2,1] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[2,2,2,1] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,1] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,1] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,1] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,1] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,2,1] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,1,1,3,1] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[2,1,3,1] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,2,3,1] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,2,3,1] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[3,3,1] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,1,1,3,1] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[2,1,3,1] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,1,1,3,1] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,1,1,3,1] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[2,1,3,1] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,2,3,1] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,2,3,1] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,2,3,1] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[3,3,1] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,1,1,3,1] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[2,1,3,1] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,1,1,3,1] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,1,1,3,1] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[2,1,3,1] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,1,1,3,1] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,1,1,3,1] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,1,1,3,1] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[2,1,3,1] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,2,3,1] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,2,3,1] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,2,3,1] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,2,3,1] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[3,3,1] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,1,4,1] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[2,4,1] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,1,4,1] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,1,4,1] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[2,4,1] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,1,4,1] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,1,4,1] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,1,4,1] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[2,4,1] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,1,4,1] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,1,4,1] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,1,4,1] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,1,4,1] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[2,4,1] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,5,1] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,5,1] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,5,1] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,5,1] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,5,1] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[6,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,1,2] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,2,1,2] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,2,1,2] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,3,1,2] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,3,1,2] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[1,3,1,2] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,1,2] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,2,2] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,2,2] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,2,2] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,2,2] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[1,2,2,2] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,2,2] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,1,3,2] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,3,2] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,1,3,2] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,1,3,2] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,3,2] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,1,3,2] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,1,3,2] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[1,1,3,2] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,3,2] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,4,2] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,4,2] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[1,4,2] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[1,4,2] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[5,2] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,1,2] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,2,1,2] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,2,1,2] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,3,1,2] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,3,1,2] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[1,3,1,2] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,1,2] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,1,2] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[1,2,1,1,2] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,1,2] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,2,1,2] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,2,1,2] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[1,1,2,1,2] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[1,1,2,1,2] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[1,1,2,1,2] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,2,1,2] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,3,1,2] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,3,1,2] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[1,3,1,2] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[1,3,1,2] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,1,2] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,2,2] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,2,2] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,2,2] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,2,2] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[1,2,2,2] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,2,2] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[1,1,1,2,2] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,2,2] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[1,1,1,2,2] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[1,1,1,2,2] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,2,2] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[1,1,1,2,2] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[1,1,1,2,2] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[1,1,1,2,2] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,2,2] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[1,2,2,2] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[1,2,2,2] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[1,2,2,2] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[1,2,2,2] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[3,2,2] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,1,3,2] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,3,2] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,1,3,2] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,1,3,2] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,3,2] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,1,3,2] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,1,3,2] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[1,1,3,2] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,3,2] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,1,3,2] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,1,3,2] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[1,1,3,2] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[1,1,3,2] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,3,2] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,4,2] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,4,2] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[1,4,2] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[1,4,2] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[1,4,2] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[5,2] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,1,1,3] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,1,3] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,1,3] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,1,3] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,1,2,3] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,2,3] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,1,2,3] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,1,2,3] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,2,3] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[1,3,3] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[1,3,3] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[1,3,3] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,3] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,1,1,3] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,1,3] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,1,3] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,1,3] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,1,1,3] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,1,1,3] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,1,3] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,1,3] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[1,2,1,3] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,1,3] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,1,2,3] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,2,3] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,1,2,3] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,1,2,3] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,2,3] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[1,1,2,3] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[1,1,2,3] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[1,1,2,3] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[2,2,3] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[1,3,3] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[1,3,3] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[1,3,3] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[1,3,3] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,3] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,1,1,3] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,2,1,3] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,2,1,3] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,3] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,1,1,3] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,1,1,3] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,2,1,3] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,2,1,3] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[1,2,1,3] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,3] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[2,1,1,3] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[2,1,1,3] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[1,1,1,1,3] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[1,1,1,1,3] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[1,1,1,1,3] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[2,1,1,3] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[1,2,1,3] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[1,2,1,3] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[1,2,1,3] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[1,2,1,3] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,3] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[1,1,2,3] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[2,2,3] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[1,1,2,3] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[1,1,2,3] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[2,2,3] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[1,1,2,3] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[1,1,2,3] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[1,1,2,3] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[2,2,3] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[1,1,2,3] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[1,1,2,3] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[1,1,2,3] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[1,1,2,3] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[2,2,3] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[1,3,3] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[1,3,3] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[1,3,3] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[1,3,3] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[1,3,3] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[4,3] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,1,1,4] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,1,4] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,2,4] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,2,4] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[3,4] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,1,1,4] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,1,4] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,1,1,4] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,1,1,4] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,1,4] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,2,4] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,2,4] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[1,2,4] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[3,4] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,1,1,4] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,1,4] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,1,1,4] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,1,1,4] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,1,4] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,1,1,4] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,1,1,4] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[1,1,1,4] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[2,1,4] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,2,4] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,2,4] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[1,2,4] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[1,2,4] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[3,4] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,1,1,4] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,1,4] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,1,1,4] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,1,1,4] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,1,4] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,1,1,4] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,1,1,4] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[1,1,1,4] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[2,1,4] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,1,1,4] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,1,1,4] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[1,1,1,4] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[1,1,1,4] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[2,1,4] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,2,4] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,2,4] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[1,2,4] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[1,2,4] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[1,2,4] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[3,4] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[1,1,5] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,5] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[1,1,5] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[1,1,5] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,5] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,1,5] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,1,5] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[1,1,5] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[2,5] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,1,5] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,1,5] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[1,1,5] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[1,1,5] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[2,5] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[1,1,5] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[1,1,5] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[1,1,5] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[1,1,5] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[1,1,5] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[2,5] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,6] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,6] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[1,6] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[1,6] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[1,6] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[1,6] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1] [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,1,2,2,1,1] [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,2,1,1,2,1] [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,3,3,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,1,1,1,2] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2] [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,2,2] [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,4,2] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[6,2] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,1,1,3] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[2,2,4] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,4] [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,3,2,5,4,1,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[2,2,4] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[2,6] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8]
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.